Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces.
The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.
This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.
Auflage
Sprache
Verlagsort
Verlagsgruppe
Elsevier Science Publishing Co Inc
Zielgruppe
Für höhere Schule und Studium
Junior/Senior level courses, introductory courses for graduate students, individual study by mathematicians and by those in applied areas such as physics.
Illustrationen
Approx. 200 illustrations
Maße
Höhe: 235 mm
Breite: 162 mm
Dicke: 34 mm
Gewicht
ISBN-13
978-0-12-088735-4 (9780120887354)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Barrett O'Neill is currently a Professor in the Department of Mathematics at the University of California, Los Angeles. He has written two other books in advanced mathematics.
Autor*in
University of California, Los Angeles, California, U.S.A.
Chapter 1: Calculus on Euclidean Space:
Euclidean Space. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Differential Forms. Mappings.
Chapter 2: Frame Fields:
Dot Product. Curves. The Frenet Formulas. ArbitrarySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. The Structural Equations.
Chapter 3: Euclidean Geometry:
Isometries of R3. The Tangent Map of an Isometry. Orientation. Euclidean Geometry. Congruence of Curves.
Chapter 4: Calculus on a Surface:
Surfaces in R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Forms. Topological Properties. Manifolds.
Chapter 5: Shape Operators:
The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit Case. Special Curves in a Surface. Surfaces of Revolution.
Chapter 6: Geometry of Surfaces in R3:
The Fundamental Equations. Form Computations. Some Global Theorems. Isometries and Local Isometries. Intrinsic Geometry of Surfaces in R3. Orthogonal Coordinates. Integration and Orientation. Total Curvature. Congruence of Surfaces.
Chapter 7: Riemannian Geometry: Geometric Surfaces. Gaussian Curvature. Covariant Derivative. Geodesics. Clairaut Parametrizations. The Gauss-Bonnet Theorem. Applications of Gauss-Bonnet.
Chapter 8: Global Structures of Surfaces: Length-Minimizing Properties of Geodesics. Complete Surfaces. Curvature and Conjugate Points. Covering Surfaces. Mappings that Preserve Inner Products. Surfaces of Constant Curvature. Theorems of Bonnet and Hadamard.
